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If x is a positive integer, is 6 a factor of x? 1) 6 is a factor of 3x

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If x is a positive integer, is 6 a factor of x? 1) 6 is a factor of 3x  [#permalink]

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New post Updated on: 11 Apr 2017, 19:32
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If x is a positive integer, is '6' a factor of x?

1) 6 is a factor of 3x
2) 12 is a factor of \(x^2\)

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Originally posted by hazelnut on 24 Mar 2017, 04:54.
Last edited by Vyshak on 11 Apr 2017, 19:32, edited 1 time in total.
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Re: If x is a positive integer, is 6 a factor of x? 1) 6 is a factor of 3x  [#permalink]

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New post 24 Mar 2017, 07:45
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ziyuen wrote:
If x is a positive integer, is 6a factor of x?

1) 6 is a factor of 3x
2) 12 is a factor of \(x^2\)


It seems you've got unlimited source of good questions.

1) 6 is a factor of 3x

\(3x = 6y\)

\(x = 2y\)

\(x=2n\), \(y=n\), where \(n\) is any integer. \(x\) may or may not be a multiple of \(6\). Insufficient.

2) 12 is a factor of \(x^2\)

\(x^2 = 12y\)

\(x = \sqrt{12y} = 2*\sqrt{3y}\).

For \(x\) to be an integer min value of \(y\) should be \(3\), hence min value of \(x=6\). Sufficient.

Answer B.
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Re: If x is a positive integer, is 6 a factor of x? 1) 6 is a factor of 3x  [#permalink]

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New post 11 Apr 2017, 14:24
I don't agree with the OA...
we are asked:
is 6a factor of x?
we are given 0 information about a.
a can be infinite - so how 6*a is a factor of x?
E should be the answer.

otherwise, if we are not asked for 6a where a is a coefficient - edit the question, as it creates confusion
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Re: If x is a positive integer, is 6 a factor of x? 1) 6 is a factor of 3x  [#permalink]

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New post 11 Apr 2017, 14:38
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mvictor wrote:
I don't agree with the OA...
we are asked:
is 6a factor of x?
we are given 0 information about a.
a can be infinite - so how 6*a is a factor of x?
E should be the answer.

otherwise, if we are not asked for 6a where a is a coefficient - edit the question, as it creates confusion


There's a typo on the OP.
"6a" should be "6 a"

I originally read it as "6a" also.

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Re: If x is a positive integer, is 6 a factor of x? 1) 6 is a factor of 3x  [#permalink]

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New post 15 Apr 2017, 21:32
1) x can be = 2,4,6,8 ... not sufficient
2) since x^2 could be = 12, 24,36,48,60 there are only a few combinations when x is integer => then 6 is definitely a factor of x
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Re: If x is a positive integer, is 6 a factor of x? 1) 6 is a factor of 3x &nbs [#permalink] 15 Apr 2017, 21:32
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